Differential virial theorem in density-functional theory in terms of the Pauli potential for spherically symmetric electron densities: Illustrative example for the family of Be-like atomic ionsDifferential virial theorem in density-functional theory in terms of the Pauli potential for spherically symmetric electron densities: Illustrative example for the family of Be-like atomic ions

The differential virial theorem relates the force −V/r associated with the one-body potential V(r) of density-functional theory to the Laplacian 2n of the ground-state density n(r) and to a quantity zs(r) involving the kinetic energy density tensor t(r). Having the concept of the Pauli potential VP(r), zs is derived for spherically symmetric ground-state densities n(r) in terms of the von Weizsäcker kinetic energy density and the first derivative of VP(r). zs is related solely to the gradient kinetic energy density tG(r) for Be-like atomic ions.